Know Your Thermo

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Describe the reaction below.

PCl3(g) + Cl2(g) -> PCl5(g); Delta(Hf) = -87.9kJ/mol

A. spontaneous at all temperatures

B. nonspontaneous at all temperatures

C. ΔGrxn < 0 at only low temperatures

D. spontaneous at only high temperatures

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Correct Answer: C.Delta(Grxn) < 0 at only low temperatures

On the MCAT, numbers can be intimidating, but remember that if the answer choices have no numbers in them, we should think conceptually instead of empirically. Gibbs equation helps us determine if a reaction is spontaneous or non-spontaneous. It is given as:G = H – TS

In this case, the enthalpy change H is a negative number (exothermic). We know that the entropy change (S) is also negative (the products are more ordered than the reactants) because the reactants are 2 moles of gas and the products are only 1 mole of gas (a synthesis of phosphorus pentachloride). Our equation now be read differently as:
G = (negative number) – temperature * (negative number)

Temperature is in Kelvin and thus always a positive number, but we must consider two possibilities regarding temperature: (1) If this positive temperature is relatively low, the second part of the equation is a small positive number. Thus, if you add a small positive number to a negative number, it will probably still be negative (G<0). (2) If the positive temperature is relatively high, the second part of the equation is a large positive number. If you add a large positive number to a negative number, it will probably become positive (G>0).

In both these cases, ambiguity is important because we don’t know the temperature or S. The only answer that appropriately describes the case we have here is C.

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